Question

Help me ill give 100 pts

Answer 1

Answer:

Small pizza is for 1 person, Large pizza is for 5 people

Skills needed: System of Equations

Step-by-step explanation:

1) First, let's make two variables:

--> $l$ = how many people a large pizza can feed

--> $s$ = how many people a small pizza can feed

2) We need to use a system of equations to solve this --> A system is 2 or more equations with specific solutions for the variables involved.

Example:

$y=x+5$

$y+x=10$

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We can solve with elimination:

$y-x=5 \\ y+x=10$

(Rewriting the first equation to look like the second one)

---> Then we add both:

$y-x=5 \\ y+x=10 \\ 2y=15 \\ y= 7.5$

When we add both equations, we eliminate the variable $x$, solving for $y$ easily. After this, we can solve for

---> $y+x=10 \\ 7.5+x=10 \\ x=2.5$

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This is the elimination method of a system (Note: we can also subtract equations if needed)

3) Let's make a system for this problem:

$3s+2l=13$ ---> 3 small pizzas (multiplied by the number of people it can feed) + 2 large pizzas (multiplied by the number of people it can feed) is for 13 people.

$3s+4l=23$ ---> 3 small pizzas (multiplied by the number of people it can feed) + 4 large pizzas (multiplied by the number of people it can feed) is for 23 people.

4) We have two equations:

$3s+2l=13 \\ 3s+4l=23$

We can eliminate $s$ by subtracting both equations.

---> $3s+2l=13 \\ 3s+4l=23 \\ -2l=-10 \\ l=5$

We subtracted $3s$ from $3s$ which is just 0 (so it does not have to be shown)

We subtracted $4l$ from $2l$ which is just $-2l$

On the right side: $23$ subtracted from $13$ which is just $-10$

----> $-2l=-10$, divide by -2, $-10 \div -2 = 5$

$l=5$, which means a large pizza is for 5 people.

$3s+2l=13 \\ 3s+2(5)=13 \\ 3s+10=13 \\ 3s=3 \\ s=1$

Substituting $l$ into the first equation (it does not matter which one you substitute into) will get $s=1$

Small pizza is for 1 person.